ShiveshM / FiniteDifferenceComputing

Finite Difference Computing

Finite Difference Computing

Notes from Langtangen's "Finite Difference Computing with Exponential Decay Models", published by Springer.

Chapters

1. Algorithms and implementations
   • The Forward Euler scheme
   • The Backward Euler scheme
   • The Crank-Nicolson scheme
   • The unifying / theta-rule
   • Numerical Error
   • Differentiate
   • Integrate
2. Analysis
   • Experimental investigations
   • Stability
   • Accuracy
   • Amplification error
   • Global error
   • Global integrated error
   • Truncation error
   • Consistency, stability, and convergence
   • Model errors
   • Data errors
   • Discretisation errors
   • Rounding errors
   • Exponential growth
3. Generalisations
   • Include variable coefficient and source term
   • Verification
   • Convergence
   • Systems of ODEs
   • Generic first-order ODEs
   • Implicit 2-step backward scheme
   • Leapfrog schemes
   • 2nd-order Runge-Kutta method
   • 2nd-order Taylor-series method
   • The 2nd- and 3rd-order Adams-Bashforth schemes
   • 4th-order Runge-Kutta method
4. Models
   • Scaling and dimensionless variables

Dependencies

• Python >= 3.7
• NumPy
• SciPy
• SymPy
• Matplotlib

Usage

Overview of chapters is given above. To run all code for a particular chapter, e.g. chapter 1, simply run

python chap1.py

To specify a particular method(s), then enter the name of the method after the filename, e.g. to run the methods forward_euler and backward_euler inside chap1.py, do

python chap1.py forward_euler backward_euler